Question

Assuming that the earth is revolving around the sun in circular orbit of radius 'R', the angular momentum is directly proportional to rⁿ. The value of 'n' is ______.

Options

• `1/3`

• `1/2`

• `1/4`

• 1

Answer 1

Assuming that the earth is revolving around the sun in circular orbit of radius 'R', the angular momentum is directly proportional to rⁿ. The value of 'n' is `underline(1/2)`.

Explanation:

Angular momentum L = m v R

Now `"mv"^2/"R" = "GMm"/"R"^2`

`"v"^2 = "GM"/"R"`

`"v" = sqrt("GM"/"R")`

∴ L = m`sqrt("GM"/"R") xx "R" = "m"sqrt("GMR")`

∴ L ∝ R^1/2